{"id":47763,"date":"2025-07-02T15:35:22","date_gmt":"2025-07-02T15:35:22","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=47763"},"modified":"2025-07-02T15:35:24","modified_gmt":"2025-07-02T15:35:24","slug":"find-the-rate-of-change-of-the-area-of-a-square-with-respect-to-the-length-of-a-side-when-the-side-is-5cm-long","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-rate-of-change-of-the-area-of-a-square-with-respect-to-the-length-of-a-side-when-the-side-is-5cm-long\/","title":{"rendered":"Find the rate of change of the area of a square with respect to the length of a side, when the side is 5cm long"},"content":{"rendered":"\n<p>Find the rate of change of the area of a square with respect to the length of a side, when the side is 5cm long<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The rate of change of the area of a square with respect to the length of a side can be found by differentiating the area formula with respect to the side length.<\/p>\n\n\n\n<p>The area AA of a square is given by: A=s2A = s^2<\/p>\n\n\n\n<p>Where ss is the length of a side of the square. To find the rate of change of the area with respect to the side length, we differentiate AA with respect to ss: dAds=dds(s2)\\frac{dA}{ds} = \\frac{d}{ds}(s^2)<\/p>\n\n\n\n<p>Using the power rule of differentiation: dAds=2s\\frac{dA}{ds} = 2s<\/p>\n\n\n\n<p>This means that the rate of change of the area of the square with respect to the length of a side is 2s2s, where ss is the side length.<\/p>\n\n\n\n<p>Now, we are asked to find the rate of change when the side is 5 cm long. Substituting s=5s = 5 into the equation: dAds=2(5)=10\u2009cm2\/cm\\frac{dA}{ds} = 2(5) = 10 \\, \\text{cm}^2\/\\text{cm}<\/p>\n\n\n\n<p>Therefore, the rate of change of the area of the square with respect to the length of a side when the side is 5 cm long is 10\u2009cm2\/cm10 \\, \\text{cm}^2\/\\text{cm}.<\/p>\n\n\n\n<p>In simpler terms, for every 1 cm increase in the side length, the area of the square increases by 10 square centimeters when the side is 5 cm long. This result shows how sensitive the area of a square is to changes in the side length, highlighting the quadratic nature of the area formula.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the rate of change of the area of a square with respect to the length of a side, when the side is 5cm long The correct answer and explanation is: The rate of change of the area of a square with respect to the length of a side can be found by differentiating the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-47763","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/47763","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=47763"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/47763\/revisions"}],"predecessor-version":[{"id":47764,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/47763\/revisions\/47764"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=47763"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=47763"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=47763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}